Fast and accurate estimation of target range, range rate (i.e., radial velocity), and acceleration from sampled radar return signals is necessary for some radar applications. Similarly, accurate estimation of the motion parameters of a moving platform, such as an aircraft, having a radar system therein is crucial for accurate estimation of a “point of interest” on the ground. For example, joint estimation of these target or platform motion parameters is an important precursor to motion compensation for high resolution spectral analysis of targets and synthetic aperture radar (SAR) processing. The joint estimation of platform motion parameters is also applicable in SAR imaging of landing areas during degraded visual conditions. For example, the military continues to suffer both equipment damage and injury to personnel due to mishaps when landing in degraded visual environments (DVEs).
There are air-to-ground applications, such as SAR imaging applications, that rely on information from an Inertial Navigational System (INS) to produce well focused images. An INS is a navigation aid that uses a computer, motion sensors (accelerometers) and rotation sensors (gyroscopes) to continuously calculate the position, orientation, and velocity (direction and speed of movement) of a moving object without the need for external references. However, current INS systems have measurement biases that can substantially impact the quality of the formed SAR images.
Many conventional radar systems attempt to accurately and expeditiously estimate target motion parameters. Some techniques used by conventional systems include the maximum entropy technique, the phase-gradient autofocus technique, and the phase difference autofocus technique, among others. However, a canonical autofocus technique may not be used to correct the INS errors, because of spatially varying quadratic phase in wide area imaging applications. Furthermore, INS accuracy may not be sufficient for imaging at the some short wavelengths, for example, Ku band wavelengths (˜2 cm). Moreover, large scene size (for example, 300 m×300 m) relative to range, requires that corrections to INS data be made relative to the scene center (i.e., point of interest).
Maximum likelihood estimation (MLE) is a popular statistical method used to calculate the best way of fitting a mathematical model to some data. Modeling real data by estimating a maximum likelihood offers a way of tuning the free parameters of a model to provide an optimum fit. As a result, some conventional systems have utilized the MLE technique for the determination of target motion parameters. In these cases, the MLE reduces to finding the maximum of a nonlinear 3-dimensional (3D) likelihood function. The range-velocity projection of the likelihood function behaves like an ambiguity function with a main lobe accompanied by surrounding side lobes that introduce many local maxima. The extent of the main lobe is given by the radar range and velocity resolution formulas, known to those skilled in the art. The MLE technique is used in some embodiments of this invention because of its high accuracy and robustness in the presence of noise.